The Pauli Exclusion Principle

The Pauli Exclusion Principle

See what happens when you click on lithium (Li)--that's element number three in the periodic table.

There are three electrons, all right--but why is the yellow one so much higher up on the chart? In the picture, it looks like that one is a lot farther away from the nucleus than the others...hey, does that mean it's in

a higher energy level?

Exactly. If you move the mouse over any electron on the chart, you'll see a little blue number appear above it. This tells you, in eV, how much energy it would take to free that electron from the clutches of

the nucleus. In the case of the outermost electron, this is called the ionization energy.

Hmm...the electrons in the lower row have higher numbers listed. I guess that makes sense--the closer they are to the nucleus, the more strongly the electric

force would be pulling them in. But that means the electrons in higher energy levels have lower numbers on the chart...

The terminology is a little confusing, I agree. Think of it this way: the more energy of its own an electron has, the less additional energy it needs in order to

escape.

Okay, so why is that third electron in a higher level than the first two? Why not just add it to the lowest one?

Because the lowest level is "full"; it can't hold more than two electrons.

Why? That sounds totally arbitrary to me.

The rule that's operating here is called the Pauli exclusion principle, first proposed by Wolfgang Pauli. Pauli guessed that two electrons can't be in the same "quantum state"--

I'll explain more fully what that means later. In this context, it means that two identical electrons can't be in the same energy level in the same atom.

But you just told me that the lowest energy level can hold two electrons.

Ah, yes--two electrons that are not identical. They differ in a characteristic called spin...

Spin

Spin? What's that?

Well, it's an additional property that electrons (and other particles) possess. Here's an analogy: think about the Earth orbiting the sun--

Haven't you just been pounding into my head that electrons don't orbit like planets?

It's true, they don't--and yet that picture remains helpful and illuminating in many contexts. So bear with me for a moment: think about the Earth. Not only does it orbit around the sun once a year, it's

also spinning once a day on its own axis...

And that's what spin is! Although I suppose you're going to tell me that electrons don't really spin, any more than they really orbit.

You catch on quickly. They don't spin--but it's tremendously useful to think about them as if they did, and for most practical purposes, you can. In the present case, think of the two electrons in that lowest

energy level as spinning in opposite directions. It's often

said that one has "spin up" and the other "spin

So each level has room for a spin up and a spin down--that makes sense. But you haven't explained s, p, and d yet; there must be more complications

to worry about.

Indeed...

Electron Configurations Continued

Take a look at the elements beyond lithium and see what you can discover.

Let's see...the fourth element, beryllium (Be), has a second electron in the higher energy level, which means that level now has both a spin up and a spin

down. So the next element should begin a third energy level--is that right?

See for yourself. Try clicking on boron (B), the fifth element--you know, the one Bruce Willis was so excited about.

Hey, what's going on? The fifth electron has a slightly higher energy than the other yellow ones, but it's not directly above them; it's in that column labeled "p."

Ah. Do you have any ideas about what might be happening?

Well...my best guess is that the colored rows, pink and yellow, represent the main energy levels, and s, p, and d are like smaller sublevels of them.

Very good. So what do you think is going to happen as you keep going along that row of the periodic table?

Hmm...carbon (C) has a second electron in the p column, so now s and p in the yellow row each have a spin up and a spin down. The next electron must start a whole new energy level, or maybe it goes into the d column, if that's the next higher sublevel.

Sounds very logical...but now look at nitrogen (N).

Hey, the seventh electron went into the p column too! How can there be three with the same energy?

It gets worse. Go on.

Oxygen (O), fluorine (F), neon (Ne)--more electrons just keep getting stuffed into that same state. What

happened to the exclusion principle? This makes no sense at all!

It makes perfect sense, once you know the rules.

Rules for Electron Configurations

I wish you'd stop being so mysterious and explain these "rules" you keep referring to.

I was just about to do that. I have to warn you, though, that the rules may seem arbitrary to you, and I won't be giving any satisfactory explanation of the reasons for them. Partly that's because I want

to spare you a lot of complicated math, and partly it's because this is just the way nature is. I'll just ask you to have faith that all this numerology comes out of a sophisticated mathematical theory, and has been upheld time after time by experiment.

I can, if you like, tell you about quantum numbers; they provide a more quantitative way of understanding these rules.

For now I think I'll be satisfied if you can tell me how to predict those electron arrangements you've been showing me.

I can do that. First of all, you were correct when you

guessed that those colored rows in the chart correspond to the "main energy levels"; they're often called primary energy levels, incidentally. Usually, a higher row means a higher energy, and energy gaps between rows tend to be quite large, in comparison with the gap

between, say, s and p.

Are you ever going to explain what s and p mean?

I'll do that right now. As you surmised, the s, p, and d columns represent smaller "sublevels" of the primary

rows...

Then why not just call them A, B, and C, or something else at least vaguely logical?

This is a bit of archaic notation left over from nineteenth century spectroscopy--rather silly, but everyone uses it, so we're stuck with

it. If you must know, s stands for "sharp," p is for "principal," and d is for "diffuse"--supposedly they refer to the appearance of various spectral lines. The next one is called f, for "fundamental"; mercifully, the subsequent ones just go alphabetically: g, h, etc.

Electron Clouds and Energy Levels

Okay, so why is it that s only holds two electrons, but p has room for six?

Well...remember that each electron is existing in one of those strange probability clouds, which, as you've seen, can have widely varying shapes and sizes. Another statement

of the Pauli exclusion principle I mentioned is this: no two electrons in an atom can be in the same type of cloud with the same spin.

So you're saying that p electrons have more cloud shapes available to them?

Precisely. It happens that s clouds are always spherical; the spheres just get bigger as the primary energy level

increases.

However, p and d states are more interesting: there can be several different-shaped clouds at the same energy. For example, here are two p states from the second primary level:

It turns out that there are three kinds of p clouds in each primary level.

...and each one can hold a spin up and a spin down, so that's why six electrons fit into the p column!

Very good. You can think of each electron's "quantum state," its full, unique description, as being the sum of a particular probability cloud plus a spin:

+

A certain d state in the third primary level

spin down

Futhermore, there are five different shapes for d (hence room for ten electrons), and seven in the next sublevel, f...I hope you're noticing a pattern here. (If you want to know more about where these numbers come from, go ask Dr. Mahan about quantum numbers.)

Electron Configurations and the Periodic Table

I understand the rules so far, but I still have a lot of questions. First of all, I can see from the chart that the lowest row only has s electrons, but the next row has electrons in both the s level and the p level, or whatever

you're supposed to call them...

"Sublevel" is fine; you can also speak of electrons' being in s or p "states." You'll frequently hear these states called orbitals, especially in chemistry. Of course, that term can be a little confusing--

Yeah, yeah, I know--because electrons don't really orbit.

Good, you've been paying attention. Incidentally, the s states in the first primary level

are called 1s orbitals, those in the second row 2s, and so forth.

Now, to return to your question: another rule you'll have to remember is that the number of sublevels increases with each primary energy level. The first row has just s orbitals, the second has s and p, the third s, p, and d, and so forth.

The way the periodic table is arranged is starting to make sense to me now. The rows of the table match up with the

primary energy levels--that's why the first row only has two elements. In the second row, lithium and beryllium are filling the two 2s spots; then there's a big space because the next six elements are filling the 2p

orbitals.

That's exactly right. Now look at the third row; is it the way you'd expect it to be?

Hmm...sodium (Na) and magnesium (Mg) add the two 3s electrons, and then the next

six elements, up to argon (Ar), fill the 3p orbitals. That's all fine, but why does the row end there? This row should have a d sublevel, too, if you were telling the truth.

I never lie--but I won't deny that there are more subtleties I haven't yet revealed to you.

Click on potassium (K), the first element in the fourth row.

Hey! Now there's an electron in an 4s state, and still nothing in the 3d orbitals. How do you

explain that?

Electron Configurations

and the Periodic Table II

I've never come right out and said

this, but I'm sure you've noticed that the energy levels get filled in order from lowest energy to highest; when you add a new electron, it goes into the lowest-energy state that's available.

Sure, that's pretty obvious.

That's why I thought the next electron for potassium would

go into a d orbital instead of up to a whole new row--you said that a higher primary level always means a higher energy.

I

said usually, not always. The energy levels aren't always so well-behaved as one might like; it sometimes happens that the first

orbitals in a "higher" primary level actually have less energy than the top orbitals of the level below.Click on the advanced button to find out why this occurs.

So in

potassium, the 4s orbitals end up with less energy than the 3d states--that's why

potassium starts a new row in the periodic table. I bet calcium (Ca) puts an electron in that second 4s orbital...yup, it does.

Okay, now click on scandium

(Sc).

Now the 3d orbitals are getting some

attention! All those elements from scandium through zinc (Zn) are just filling the ten green d spaces. Then gallium (Ga) goes back up and starts the 4p orbital.

This periodic table ends at krypton,

when the 4p orbitals are filled--but of course one can keep going. Click here to open an extended version of the periodic table, which shows the electron configurations for the elements up to 103. I'll let you play around with this and figure out the order in which the various orbitals are filled.

A note about the arrangement of elements: barium (Ba) is element number 56; element 57, lanthanum (La), begins that first separate row at the bottom, which continues up to number 71, lutetium (Lu). Number

72, hafnium (Hf), is up next to barium again. A similar thing happens in the seventh row of the table. Look at the electron configurations and see if you can tell why these elements are arranged in this way.

A Chemists' Perspective on the Periodic Table

All right, I think I understand now why the periodic table is laid out the way it is. The rows go with the primary energy levels...

1

1

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44444444444444445555555555555555556666

66666666666666776666666666666677777777

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...and there are different sections of the table that go with the different sublevels.

That's right; you can think of the table as being divided into "blocks" like this:

s ss s p p p p p ps s p p p p p ps s d d d d d d d d d d p p p p p ps s d d d d d d d d d d p p p p p ps s d d d d d d d d d d p p p p p ps s

f f f f f f f f f f f f f ff f f f f f f f f f f f f f

That makes so much sense! Now I can see why someone had the idea of putting the elements in a table like this; once you know how the electron configurations work, this arrangement wouldn't be so hard to come up with.

Actually, the first designer of the periodic table knew nothing about energy levels or even electrons; at the time, hardly anything was known about the

structure of atoms.

Really? Then how would anyone know which elements to put where?

Well, that's quite an interesting story. You see, there's more to the periodic table than just electron configurations. Up until now I've been giving you a physicist's view--from the bottom up, so to speak. Now we'll look at the periodic table from a chemist's perspective, from the top down

The Origin of the Periodic Table

I know what the periodic table looks like, but where did it come from? Whose idea was it to arrange the elements this way?

In 1869, a Russian chemist named Dmitri Mendeleev came up with a way of organizing the elements that were known at the time.

He set them out in order of atomic weight, and then grouped them into rows and columns based on their chemical and physical properties.

1869...that's way before the Schrödinger model, or even the Rutherford model.

That's right. Mendeleev had no idea what atoms were made of or why they behaved as they did. Nevertheless, he was able to put together the periodic table almost as we know it today--except that some

elements were missing, because they were unknown in 1869.

Based on the gaps in his table, Mendeleev even succeeded in predicting the existence and properties of several new elements.

That's pretty impressive. Can you tell me more about how Mendeleev organized the table? What kinds of properties did he use?

His basic rule was this: the elements in any column, or group, of the table are similar to their column-mates. For example, look at the first column on the

left, underneath hydrogen (H). The elements in this group are called the alkali metals; they're all soft metals that react violently with water to make hydrogen gas.

Click here if you'd like to read more about Mendeleev's methods and the chemistry of his time

Periodic Properties

Hmm...so the elements in the table are arranged in order from lightest to heaviest, and elements in the same column have

matching properties. That's right.

That means that elements whose atomic weights are really close together can be very different, and some elements with far-apart atomic weights are very similar. As you move from lighter atoms to heavier

ones, you keep periodically running across the same

properties...

Hence the name periodic table.

Oh, right.

I don't mean to pick on you; what you said was actually a very important insight. The periodic table is full of repeating patterns. Take atomic size, for instance: atoms get bigger as you move down a

column, and smaller as you move to the right across a row, or period.

That's so weird! I'd think the atoms would just get bigger as they got heavier; why do they get smaller as you move to the right?

The answer lies in the underlying structure of those atoms...

Atomic Structure and Periodic Properties

I'll show you some of the details of atomic structure using an interactive periodic table applet, which, I hope, should now have opened in another window.

If you don't already have the periodic table applet open, click here:

to open it now.

After Mendeleev's time, scientists discovered what you already know: an atom consists of a positively charged nucleus, made of

neutrons and protons, and some negatively charged electrons swarming around it.

But what exactly is the configuration of those electrons? That's the key to understanding why each element behaves the way it does.

"Configuration"? I'm not sure I understand what that means. Does it have something to do with that chart in the applet, the one that says "s p d" at the top?

Yes; that chart shows how the electrons are arranged in the selected element. I'd be happy to explain in detail how the electrons organize themselves; if

you'd prefer, I can also give you a short crash course in

interpreting the chart.

Now that we've talked about the structure of atoms, can you answer my question about their sizes?

There are two patterns to be explained: atoms get bigger as you go down a group, and smaller as you go to the right across a period. The reason for the

first one shouldn't be so hard to see now; look again down the column of alkali metals in the applet.

Each time you move down, you add another primary level--lithium's highest electron is in a 2s state, for sodium it's 3s, and so on.

Exactly. And the higher an electron's energy, the farther from the nucleus it is.

So the atoms get bigger as you add electrons to higher energy levels--that makes sense. But why do they get smaller as you move to the right?

Well, you'll notice that within a period, the outermost electrons are all in the same primary level--that is, at (roughly) the same distance from the nucleus. But as

you move to the right, the elements increase in atomic number; each element has one more proton than its left-

hand neighbor. The more protons in the nucleus, the more strongly the valence electrons are pulled in...

...and so the atoms shrink! Also, I can see from the chart that the ionization energies get larger as you go to the right; that must be for the same reason.

Very good! Similarly, the ionization energies decrease as you move down a group.

Atomic Structure and Chemical Properties

You said that electron configurations are "the key to understanding why each element behaves the way it does." How does that work?

I'll give you an example: look again at that far left group with hydrogen and the alkali metals. Start at the top and go down, clicking on each element in turn; what do you notice about the electrons?

Um...well, in each one of these, the very top electron is starting a new colored row; it's all by itself in the s sublevel.

Very good! The chart will tell you that the ionization energy for that element is quite small. It wouldn't take much to send that one solitary electron sailing off into

dizzying freedom--and that sort of thing, electrons leaving their home atoms, leads directly to chemical reactions.

So that's why the alkali metals react so violently--it's easy to set them off.

Atomic Structure and Chemical Reactions

Do all elements lose their top electrons in chemical reactions?

No; sometimes the opposite happens. Take a look at the second column from the right in the periodic table--the one that

starts with fluorine (F).

These elements have their highest electrons in p orbitals--five at the

same energy. p has room for six, doesn't it?

That's right. These elements are called the halogens; they're highly reactive, too, but in a different way than the alkali

metals. What sets them off is not losing one of their own, but picking up a stray electron, which fits perfectly into that "empty space" in the p sublevel.

Wow, it sounds like the halogens and the alkali metals would be perfect for each other.

You're absolutely right; those two groups love to form compounds together. For example, I'm sure

you're familiar with sodium chloride,

NaCl.

What would the electrons look like in an element that wasn't very reactive?

Look at the far right group, with helium (He) at the top.

Except for helium, all of these have a "full" p sublevel at the top, with six electrons.

Yes. Helium, of course, has a "full" s sublevel--you may recall that the first primary level has

only s orbitals. These guys are called the noble gases, and they're perfectly happy with themselves as they are--no desire to give up or take in electrons. As a consequence, they hardly ever form compounds with other elements.

In general, the arrangement of the outermost electrons, called valence electrons, tells you all about an element's chemical behavior.